Huffman tree (optimal binary tree) & Huffman coding (c++ implementation)

Huffman tree (optimal binary tree)

• The binary tree with the smallest weighted path length is called the Huffman tree

• The leaf node with the larger weight is closer to the root node

• The smaller the weight, the farther away the leaf node is from the root node

• Always merge the two nodes with the smallest weight and the next smallest weight, and construct the tree in turn, so that the weight of the root node is the smallest weight

• If the Huffman tree has n0 leaf nodes, then the number of summary points of this tree is n=2*n0-1

typedef struct{
    
    
    int weight;
    int parent;
    int lchild;
    int rchild;
}HNode;

void Create_HuffMTree(HNode HFMTree[],int n){
    
           //n为叶子结点个数
    int x1,x2;  //x1和x2存储最小和次最小权值
    int m1,m2;  //m1和m2存储位置
    int i,j;
    for(i=0;i<2*n-1;++i){
    
           //HFMTree 初始化
        HFMTree[i].weight=0;
        HFMTree[i].lchild=-1;
        HFMTree[i].rchild=-1;
        HFMTree[i].parent=-1;
    }
    for(i=0;i<n;++i)
        cin>>HFMTree[i].weight; //输入n个叶子节点的权值
    for(i=0;i<n-1;++i){
    
    
        x1=x2=INT_MAX;
        m1=m2=0;
        for(j=0;j<n+i;++j){
    
    
            if(HFMTree[i].parent==-1&&HFMTree[j].weight<x1){
    
    
                x2=x1;
                m2=m1;
                x1=HFMTree[j].weight;
                m1=j;
            }
            else if(HFMTree[i].parent==-1&&HFMTree[j].weight<x2){
    
    
                x2=HFMTree[j].weight;
                m2=j;
            }
        }
        HFMTree[m1].parent=n+i;HFMTree[m2].parent=n+i;          //合并
        HFMTree[n+i].weight=HFMTree[m1].weight+HFMTree[m2].weight;
        HFMTree[n+i].lchild=m1;HFMTree[n+i].rchild=m2;
    }
}

Huffman coding (prefix coding)

• It is stipulated that the left branch in the Huffman tree represents 0, the right branch represents 1, and the sequence of 0 and 1 composed of the path branches from the root node to each leaf node is the code of the corresponding character of the node

const int n=10;         //叶子节点个数  

typedef struct{
    
    
    int bit[n];
    int start;
}HCode;

HNode HFMTree[10];          //设已经建立好的哈夫曼树已经存在HFMTree中

void HuffmanCode(HNode HFMTree[],HCode HuffCode[]){
    
    
    HCode cd;
    int i,j,c,p;
    for(i=0;i<n;++i){
    
    
        cd.start=n-1;
        c=i;
        p=HFMTree[c].parent;
        while(p!=-1){
    
    
            if(HFMTree[p].lchild==c)
                cd.bit[cd.start]=0;
            else
                cd.bit[cd.start]=1;
            cd.start--;
            c=p;
            p=HFMTree[c].parent;
        }
        for(j=cd.start+1;j<n;++j)
            HuffCode[i].bit[j]=cd.bit[j];
        HuffCode[i].start=cd.start+1;
    }
}